Search Results (116)

This paper investigates the structural properties of solutions of vector equilibrium systems and mixed variational inequalities in topological vector spaces. Based on Himmelberg-type fixed point theorem, combined with the analysis of set-valued mapping and quasi-monotone conditions, the existence criteria of solutions for two classes of generalized equilibrium problems with weak compactness constraints are constructed. This work introduces an innovative application of the measurable selection theorem of semi-continuous function space to eliminate the traditional compactness constraints, and provides a more universal theoretical framework for game theory and the economic equilibrium model. In the analysis of mixed variational problems, the topological stability of the solution set under the action of generalized monotone mappings is revealed by constructing a new KKM class of mappings and introducing the theory of pseudomonotone operators. In particular, by replacing the classical compactness assumption with pseudo-compactness, this study successfully extends the research boundary of scholars on variational inequalities, and its innovations are mainly reflected in the following aspects: (1) constructing a weak convergence analysis framework applicable to locally convex topological vector spaces, (2) optimizing the monotonicity constraint of mappings by introducing a semi-continuous asymmetric condition, and (3) in the proof of the nonemptiness of the solution set, the approximation technique based on the family of relatively nearest neighbor fields is developed. The results not only improve the theoretical system of variational analysis, but also provide a new mathematical tool for the non-compact parameter space analysis of economic equilibrium models and engineering optimization problems. This work presents a novel combination of measurable selection theory and pseudomonotone operator theory to handle non-compact constraints, advancing the theoretical framework for economic equilibrium analysis. Full article

Dock door congestion is an essential and persistent concern within the realm of outbound warehouse logistics. The inability to accommodate outbound vehicles at the loading docks, especially during peak hours, disrupts internal warehouse operations, leads to bottlenecks, and contributes to substantial additional costs and delays. This paper addresses the critical issue of dock door congestion by proposing an integrated forecast–optimization framework for its prediction and management. The framework uses advanced forecasting methods and optimization techniques to increase warehouse throughput, boost operational efficiency, and predict potential congestion events using historical and real-time data. It combines two proven methodologies, maximum entropy bootstrap (MEB) and ensemble learning via bagging, with scenario-based stochastic optimization. This hybrid approach significantly improves upon traditional models by capturing the complex, non-monotonic components and multi-seasonality inherent in warehouse throughput data. Through a detailed real-world case study, we demonstrate how the proposed approach can accurately predict the number of trucks that can be serviced within specific time windows. This information is crucial for making operational decisions, such as whether to expand the warehouse. The approach can be generalized beyond the specific case study and offers valuable insights for any logistics or supply chain operation requiring the integration of stochastic optimization with predictive modeling. Full article

Since the monotonicity of the best approximant is crucial to establish partial ordering methods, in this paper, we, respectively, characterize the best approximants in Banach function spaces and Lorentz spaces ${\mathrm{\Gamma }}_{p,w}$, in which we especially focus on the monotonicity characterizations. We first study monotonicity characterizations of the metric projection operator onto sublattices in general Banach function spaces by the property $H_g$. The sufficient and necessary conditions for monotonicity of the metric projection onto cones and sublattices are then, respectively, established in ${\mathrm{\Gamma }}_{p,w}$. The Lorentz spaces ${\mathrm{\Gamma }}_{p,w}$ are also shown to be reflexive under the condition $R{B}_p$, which is the basis for the existence of the best approximant. As applications, by establishing the partial ordering methods based on the obtained monotonicity characterizations, the solvability and approximation theorems for best proximity points are deduced without imposing any contractive and compact conditions in ${\mathrm{\Gamma }}_{p,w}$. Our results extend and improve many previous results in the field of the approximation and partial ordering theory. Full article

Edge computing (EC) plays a critical role in advancing the next-generation Industrial Internet of Things (IIoT) by enhancing production, maintenance, and operational outcomes across heterogeneous network boundaries. This study builds upon EC intelligence and integrates graph-based learning to propose a Cross-Layer Controller Tasking Scheme (CLCTS). The scheme operates through two primary phases: task grouping assignment and cross-layer control. In the first phase, controller nodes executing similar tasks are grouped based on task timing to achieve monotonic and synchronized completions. The second phase governs controller re-tasking both within and across these groups. Graph structures connect the groups to facilitate concurrent tasking and completion. A learning model is trained on inverse outcomes from the first phase to mitigate task acceptance errors (TAEs), while the second phase focuses on task migration learning to reduce task prolongation. Edge nodes interlink the groups and synchronize tasking, migration, and re-tasking operations across IIoT layers within unified completion periods. Departing from simulation-based approaches, this study presents a fully implemented framework that combines learning-driven scheduling with coordinated cross-layer control. The proposed CLCTS achieves an 8.67% reduction in overhead, a 7.36% decrease in task processing time, and a 17.41% reduction in TAEs while enhancing the completion ratio by 13.19% under maximum edge node deployment. Full article

With the deepening of degradation, the stability and reliability of the degrading system usually becomes poor, which may lead to random jumps occurring in the degradation path. A non-homogeneous jump diffusion process model is introduced to more accurately capture this type of degradation. In this paper, the proposed degradation model is translated into a state–space model, and then the Monte Carlo simulation of the state dynamic model based on particle filtering is employed for predicting the degradation evolution and estimating the remaining useful life (RUL). In addition, a general model identification approach is presented based on maximization likelihood estimation (MLE), and an iterative model identification approach is provided based on the expectation maximization (EM) algorithm. Finally, the practical value and effectiveness of the proposed method are validated using real-world degradation data from temperature sensors on a blast furnace wall. The results demonstrate that our approach provides a more accurate and robust RUL estimation compared to CNN and LSTM methods, offering a significant contribution to enhancing predictive maintenance strategies and operational safety for systems with complex, non-monotonic degradation patterns. Full article

This paper introduces a framework of hypercompositional algebra on fuzzy graphs by defining and analyzing fuzzy path-based hyperoperations. Building on the notion of strongest strong paths (paths that are both strength-optimal and composed exclusively of strong edges, where each edge achieves maximum connection strength between its endpoints), we define two operations: a vertex-based fuzzy path hyperoperation and an edge-based variant. These operations generalize classical graph hyperoperations to the fuzzy setting while maintaining compatibility with the underlying topology. We prove that the vertex fuzzy path hyperoperation is associative, forming a fuzzy hypersemigroup, and establish additional properties such as reflexivity and monotonicity with respect to $\alpha$-cuts. Structural features such as fuzzy strong cut vertices and edges are examined, and a fuzzy distance function is introduced to quantify directional connectivity strength. We define an equivalence relation based on mutual full-strength reachability and construct a quotient fuzzy graph that reflects maximal closed substructures under the vertex fuzzy path hyperoperation. Applications are discussed in domains such as trust networks, biological systems, and uncertainty-aware communications. This work aims to lay the algebraic foundations for further exploration of fuzzy hyperstructures that support modeling, analysis, and decision-making in systems governed by partial and asymmetric relationships. Full article

To investigate the impact of sand-laden flow on energy loss in Francis turbines, this study integrates entropy generation theory with numerical simulations conducted using ANSYS CFX. The mixture multiphase flow model and the SST k-ω turbulence model are employed to simulate the solid–liquid two-phase flow throughout the entire flow passage of the turbine at the Gengda Hydropower Station (Minjiang River Basin section, 103°17′ E and 31°06′ N). The energy loss characteristics under different off-design conditions are analyzed on the basis of the average sediment concentration during the flood season (2.9 kg/m³) and a median particle diameter of 0.058 mm. The results indicate that indirect entropy generation and wall entropy generation are the primary contributors to total energy loss, while direct entropy generation accounts for less than 1%. As the guide vane opening increases, the proportion of wall entropy generation initially rises and then decreases, while the total indirect entropy generation exhibits a non-monotonic trend dominated by the flow pattern in the draft tube. Entropy generation on the runner walls increases steadily with larger openings, whereas entropy generation on the draft tube walls first decreases and then increases. The variation in entropy generation on the guide vanes remains relatively small. These findings provide technical support for the optimal design and operation of turbines in sediment-rich rivers. Full article

In this paper, we propose a penalty approach for solving generalized absolute value equations (GAVEs) of the type $Ax-B\left|x\right|=b$, $(A,B\in {\mathbb{R}}^{n\times n},b\in {\mathbb{R}}^n)$. Firstly, we reformulate the GAVEs as variational inequality problems passing through an equivalent horizontal linear complementarity problem. To approximate the resulting variational inequality, a sequence of nonlinear equations containing a penalty term is then defined. Under a mild assumption, we show that the solution of the considered sequence converges to that of GAVE if the penalty parameter tends to infinity. An algorithm is developed where its corresponding theoretical arguments are well established. Finally, some numerical experiments are presented to show that our approach is quite appreciable. Full article

Energy-aware scheduling plays a critical role in modern computing and manufacturing systems, where energy consumption often increases with job execution order or resource usage intensity. This study investigates a scheduling problem in which a sequence of heterogeneous jobs—classified as either heavy or light—must be assigned to multiple identical machines with monotonically increasing slot costs. While the machines are structurally symmetric, the fixed job order and cost asymmetry introduce significant challenges for optimal job allocation. We formulate the problem as an integer linear program and simplify the objective by isolating the cumulative cost of heavy jobs, thereby reducing the search for optimality to a position-based assignment problem. To address this challenge, we propose a structured assignment model termed monotonic machine assignment, which enforces index-based job distribution rules and restores a form of functional symmetry across machines. We prove that any feasible assignment can be transformed into a monotonic one without increasing the total energy cost, ensuring that the global optimum lies within this reduced search space. Building on this framework, we first present a general dynamic programming algorithm with complexity $O\left(n^2{m}^2\right)$. More importantly, by introducing a structural correction scheme based on misaligned assignments, we design an iterative refinement algorithm that achieves global optimality in only $O\left(n{m}^2\right)$ time, offering significant scalability for large instances. Our results contribute both structural insight and practical methods for optimal, position-sensitive, energy-aware scheduling, with potential applications in embedded systems, pipelined computation, and real-time operations. Full article

Ship weather routing is heavily dependent on weather forecasts. However, the predictive nature of meteorological models introduces an unavoidable level of uncertainty which, if not accounted for, can compromise navigational safety, operational efficiency, and environmental impact. This study examines the temporal degradation of forecast accuracy across certain oceanographic and atmospheric variables, using a six-month dataset for the area of North Atlantic provided by the National Oceanic and Atmospheric Administration (NOAA). The analysis reveals distinct variable-specific uncertainty trends with wind speed forecasts exhibiting significant temporal fluctuation (RMSE increasing from 0.5 to 4.0 m/s), while significant wave height forecasts degrade in a more stable and predictable pattern (from 0.2 to 0.9 m). Confidence intervals also exhibit non-monotonic evolution, narrowing by up to 15% between 96–120-h lead times. To address these dynamics, a Python-based framework combines distribution-based modeling with calibrated confidence intervals to generate uncertainty bounds that evolve with forecast lead time (R² = 0.87–0.93). This allows uncertainty to be quantified not as a static estimate, but as a function sensitive to both variable type and prediction horizon. When integrated into routing algorithms, such representations allow for route planning strategies that are not only more reflective of real-world meteorological limitations but also more robust to evolving weather conditions, demonstrated by a 3–7% increase in travel time in exchange for improved safety margins across eight test cases. Full article

The inverse mixed variational inequality problem comes from classical variational inequality, and it has many applications. In this paper, we propose new algorithms to study the inverse mixed variational inequality problems in Hilbert spaces, and these algorithms are based on the generalized projection operator. Next, we establish convergence theorems under inverse strong monotonicity conditions. In addition, we also provide inertial-type algorithms for the inverse mixed variational inequality problems with conditions that differ from the above convergence theorems. Full article

Variational inequality problems (VIPs) provide a versatile framework for modeling a wide range of real-world applications, including those in economics, engineering, transportation, and image processing. In this paper, we propose a novel iterative algorithm for solving VIPs in real Hilbert spaces. The method integrates a double-inertial mechanism with the two-subgradient extragradient scheme, leading to improved convergence speed and computational efficiency. A distinguishing feature of the algorithm is its self-adaptive step size strategy, which generates a non-monotonic sequence of step sizes without requiring prior knowledge of the Lipschitz constant. Under the assumption of monotonicity for the underlying operator, we establish strong convergence results. Numerical experiments under various initial conditions demonstrate the method’s effectiveness and robustness, confirming its practical advantages and its natural extension of existing techniques for solving VIPs. Full article

This paper addresses the challenge of solving quasi-variational inequalities (QVIs) by developing and analyzing a forward–backward–forward algorithm from a continuous and iterative perspective. QVIs extend classical variational inequalities by allowing the constraint set to depend on the decision variable, a formulation that is particularly useful in modeling various problems. A critical computational challenge in these settings is the expensive nature of projection operations, especially when closed-form solutions are unavailable. To mitigate this, we consider the moving set case and propose a forward–backward–forward algorithm that requires only one projection per iteration. Under the assumption that the operator is strongly monotone, we establish that the continuous trajectories generated by the corresponding dynamical system converge exponentially to the unique solution of the QVI. We extend Tseng’s well-known forward–backward–forward algorithm for variational inequalities by adapting it to the more complex framework of QVIs. We prove that it converges when applied to strongly monotone QVIs and derive its convergence rate. We perform numerical implementations of our proposed algorithm and give numerical comparisons with other related gradient projection algorithms for quasi-variational inequalities in the literature. Full article

When large-scale and clustered distributed photovoltaic devices are connected to an active distribution network, the safe and stable operation of the distribution network is seriously threatened, and it is difficult to satisfy the demand for preservation of supply. Multi-agent reinforcement learning provides an idea of zonal balance control, but it is difficult to fully satisfy operation constraints. In this paper, a multi-level control framework based on a local physical model and a multi-agent sequential update algorithm is proposed. The framework generates parameters through an upper-layer reinforcement learning algorithm, which are passed into the objective function of the lower-layer local physical model. The lower-layer local physical model will incorporate safety constraints to determine the power setpoints of the devices; meanwhile, the sequential updating algorithm is integrated into a centralized training–decentralized execution framework, which can increase the efficiency of the sample utilization and promote the monotonic improvement of the strategies. The modified 10 kV IEEE 69-node system is studied as an example, and the results show that the proposed framework can effectively reduce the total operating cost of the active distribution network, while meeting the demand of the system to preserve the supply and ensure the safe and stable operation of the system. Full article

Complex Intuitionistic Fuzzy Sets (CIFSs) are an advanced form of intuitionistic fuzzy sets that utilize complex numbers to effectively manage uncertainty and hesitation in multi-criteria decision making (MCDM). This paper introduces the Shapley Choquet integral (SCI), which is a powerful tool for integrating information from various sources while considering the importance and interactions among criteria. To address ambiguity and inconsistency, we apply the Aczel–Alsina (AA) t-norm and t-conorm, which offer greater flexibility than traditional norms. We propose two novel aggregation operators within the CIFS framework using the Aczel–Alsina Generalized Shapley Choquet Integral (AAGSCI): the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Average Generalized Shapley Choquet Integral (CIFAAWAGSCI) and the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Geometric Generalized Shapley Choquet Integral (CIFAAWGGSCI), along with their special cases. The properties of these operators, including idempotency, boundedness, and monotonicity, are thoroughly investigated. These operators are designed to evaluate complex and asymmetric information in real-life problems. A case study on selecting the optimal bridge design based on structural and aesthetic criteria demonstrates the applicability of the proposed method. Our results indicate that the proposed method yields more consistent and reliable outcomes compared to existing approaches. Full article